אודות
Quadratic and hermitian forms, Central simple algebras, Azumaya algebras and the Brauer group, Classical algebraic groups, torsors, Bruhat-Tits theory, Representation theory of reductive p-adic Lie groups and its applications to Ramanujan graphs and complexes.
פרסומים
- Counterexamples in involutions of Azumaya algebras, First, U. & Williams, B., 15 Dec 2025, In: Journal of Algebra. 684, p. 256-279 24 p.
- Irredundant generating sets for matrix algebras, Blumenthal, Y. & First, U. A., 15 Dec 2025, In: Linear Algebra and Its Applications. 727, p. 308-335 28 p.
- Spaces of generators for Azumaya algebras with unitary involution, Cantor, O. & First, U. A., Apr 2025, In: Journal of Pure and Applied Algebra. 229, 4, 107919.
- Cosystolic Expansion of Sheaves on Posets with Applications to Good 2-Query Locally Testable Codes and Lifted Codes, First, U. A. & Kaufman, T., 10 Jun 2024, STOC 2024 - Proceedings of the 56th Annual ACM Symposium on Theory of Computing. Mohar, B., Shinkar, I. & O�Donnell, R. (eds.). Association for Computing Machinery, p. 1446-1457 12 p. (Proceedings of the Annual ACM Symposium on Theory of Computing).
- Highly versal torsors, First, U. A., 2024, Amitsur Centennial Symposium, 2021. Mann, A., Rowen, L. H., Saltman, D. J., Shalev, A., Small, L. W. & Vishne, U. (eds.). American Mathematical Society, p. 129-174 46 p. (Contemporary Mathematics; vol. 800).
- An 8-periodic exact sequence of Witt groups of Azumaya algebras with involution, First, U. A., Jan 2023, In: Manuscripta Mathematica. 170, 1-2, p. 313-407 95 p.
- On the Grothendieck–Serre conjecture for classical groups, Bayer-Fluckiger, E., First, U. A. & Parimala, R., Dec 2022, In: Journal of the London Mathematical Society. 106, 4, p. 2884-2926 43 p.
- ON THE NUMBER OF GENERATORS OF AN ALGEBRA OVER A COMMUTATIVE RING, First, U. A., Reichstein, Z. & Williams, B., 1 Oct 2022, In: Transactions of the American Mathematical Society. 375, 10, p. 7277-7321 45 p.
- On the Gersten–Witt complex of an Azumaya algebra with involution, First, U. A., 1 Sep 2022, In: Journal of Algebra. 605, p. 146-178 33 p.
- On the non-neutral component of outer forms of the orthogonal group, First, U. A., Jan 2021, In: Journal of Pure and Applied Algebra. 225, 1, 106477.
- Pfister's local–global principle and systems of quadratic forms, First, U. A., Dec 2020, In: Bulletin of the London Mathematical Society. 52, 6, p. 1105-1121 17 p.
- Involutions of Azumaya Algebras, First, U. A. & Williams, B., 2020, In: Documenta Mathematica. 25, p. 527-633 107 p.
- Orders that are etale-locally isomorphic, Bayer-Fluckiger, E., First, U. A. & Huruguen, M., 2020, In: St. Petersburg Mathematical Journal. 31, 4, p. 573-584 12 p.
- On uniform admissibility of unitary and smooth representations, First, U. A. & Rüd, T., 4 Feb 2019, In: Archiv der Mathematik. 112, 2, p. 169-179 11 p.
- Azumaya algebras without involution, Auel, A., First, U. A. & Williams, B., 2019, In: Journal of the European Mathematical Society. 21, 3, p. 897-921 25 p.
- Rationally isomorphic hermitian forms and torsors of some non-reductive groups, Bayer-Fluckiger, E. & First, U. A., 25 May 2017, In: Advances in Mathematics. 312, p. 150-184 35 p.
- On the number of generators of an algebra, First, U. A. & Reichstein, Z., 1 Jan 2017, In: Comptes Rendus Mathematique. 355, 1, p. 5-9 5 p.
- Patching and weak approximation in isometry groups, Bayer-Fluckiger, E. & First, U. A., 2017, In: Transactions of the American Mathematical Society. 369, 11, p. 7999-8035 37 p.
- Categorical Realizations of Quivers, First, U. A., 2 Jun 2016, In: Communications in Algebra. 44, 6, p. 2567-2582 16 p.
- Highlights from "The Ramanujan Property for Simplicial Complexes", First, U. A., 1 Jun 2016, 23 p.
- The Ramanujan Property for Simplicial Complexes, First, U. A., 9 May 2016, 90 p.
- Witt's extension theorem for quadratic spaces over semiperfect rings, First, U. A., 1 Dec 2015, In: Journal of Pure and Applied Algebra. 219, 12, p. 5673-5696 24 p.
- Rings that are Morita equivalent to their opposites, First, U. A., 5 May 2015, In: Journal of Algebra. 430, p. 26-61 36 p.
- General bilinear forms, First, U. A., Feb 2015, In: Israel Journal of Mathematics. 205, 1, p. 145-183 39 p.
- An elementary proof that rationally isometric quadratic forms are isometric, First, U. A., Aug 2014, In: Archiv der Mathematik. 103, 2, p. 117-123 7 p.
- Hermitian categories, extension of scalars and systems of sesquilinear forms, Bayer-Fluckiger, E., First, U. A. & Moldovan, D. A., 2014, In: Pacific Journal of Mathematics. 270, 1, p. 1-26 26 p.
- Stiefel-Whitney invariants for bilinear forms, First, U. A. & Vishne, U., 1 Oct 2013, In: Linear Algebra and Its Applications. 439, 7, p. 1905-1917 13 p.
- Semi-invariant subrings, First, U. A., 5 Mar 2013, In: Journal of Algebra. 378, p. 103-132 30 p.